Beliefs and traits are all part of a character's psyche.   Each makes the character unique and defines who the character is as a character, rather than a set of stats.  Unlike many of the stats and abilities, there is no set list or best choice.  As such I will give only a few examples to avoid tainting your ideas. 

Beliefs  are the core set of values, ideals, and motivations that drive your character.  These will be explored below.  They take the form of sentences or statements.  Fulfilling or meeting these beliefs result in gaining a Dayo stone (allowing you to add a die to a roll at a later point).  Making a tough decision that breaks, shatters, or goes against such a core belief may also result in a Dayo stone.  Please choose three.  Below are some examples of beliefs.

Emotions should never be a part of decision making.

Make the best of every situation.

The will of my Aygeema is more important than my wishes.

Eat, drink, and be merry because who knows what happens next.

The innocent and defenseless must be protected at all costs.

I must discover the truth about my past.

All monsters are threats to society and should be killed on sight.

I will prove my value by great deeds.

What others believe about you is more important than the truth.

Truth must be fought for at all costs.

Eventually it all comes down to combat.

Combat is never the best option, nor will it truly solve anything.

Death is not final so pain is an illusion.  (One of the core beliefs of the Academy of Necromancy btw.)

The Council is the ideal form of government and must be defended.

All systems are corrupt so I have to work outside the system.

And so on.  Your imagination is your limit and other such motivational poster slogans...